Determination of thickness and bulk sound velocities of isotropic plates using zero-group-velocity Lamb waves

Clemens Grünsteidl,Mike Hettich,István Veres,Thomas Berer

doi:10.1063/1.5034313

Abstract

We propose a method to simultaneously determine the thickness of an isotropic plate together with the longitudinal and shear elastic wave velocities of its material. The method requires knowledge of the frequencies of two zero-group-velocity Lamb modes and one respective wavenumber. These quantities are defined by the Rayleigh-Lamb equations, which we use in an inverse problem to obtain the properties of the plate. Experimentally, the frequencies of zero-group-velocity points can be obtained at high precision by measuring the elastic response spectrum of a plate, using laser-ultrasound techniques. By shaping the excitation laser spot with a spatial light modulator, we extend this to enable measurements of the corresponding wavenumber. The introduced method is demonstrated for a homogeneous tungsten and an aluminium plate.

Highlights

We propose a method to simultaneously determine the thickness of an isotropic plate together with the longitudinal and shear elastic wave velocities of its material
These methods find their limits if the shear sound velocity should be quantified, if accessing the samples is only possible from one side, if the samples must not be brought in contact with a coupling medium, or if the bandwidth of the transducers does not provide sufficient resolution for the application
We demonstrate the method for two samples with differing elastic properties and homogeneity: A rigid tungsten plate with h 1⁄4 127 lm and an anisotropy-factor close to one and a standard, soft aluminium foil with h 1⁄4 110 lm showing rolling induced texture

Summary

Introduction

We propose a method to simultaneously determine the thickness of an isotropic plate together with the longitudinal and shear elastic wave velocities of its material. The frequencies of zero-group-velocity points can be obtained at high precision by measuring the elastic response spectrum of a plate, using laser-ultrasound techniques.

Results

Conclusion